Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner

TL;DR

This paper analytically demonstrates that a meron pair in SU(2) Yang-Mills theory can support magnetic monopole loops, providing insight into quark confinement mechanisms consistent with previous numerical findings.

Contribution

It presents an analytical solution for magnetic monopole loops supported by a meron pair, aligning with numerical lattice results and supporting the meron-based quark confinement hypothesis.

Findings

Analytical magnetic monopole loop solutions in meron backgrounds.

Supports the relevance of meron pairs as quark confiners.

Consistent with previous lattice simulations.

Abstract

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.